So now the problem is, when we 'make something' its G function goes from zero to something negative (as was just shown in two ways). This implies it should happen spontaneously, since in constant T and P the second law becomes "G goes to a minimum".

So does this say things should randomly pop into existence? Obviously there is a thinking error?

Everything enters as heat from the environment (that's the meaning of -TS in the definition of G, right? And in this case: TS > U + PV (as shown in the 2nd derivation)

But I've come to the conclusion "dS_tot > 0 <=> dG < 0" under constant P and T is only an equivalence if the system has a constant amount of particles! That's probably where I made my error. (G is still < 0, but now it just doesn't matter, really)